Neither is easier to carry than the other, both are incredibly improbably ammo loads. 250 rounds in a belt is around 4 meters in length, it is a huge stretch already in game to have the MG34 belted with that load, let alone having the gunner carry another 4 meter belt.
Do you know how many times you would have to wrap 4 meters of belting around your torso to not trip over it? Even if it was in a box, how does one hold a box in one hand and a 27 pound MG with a 250 round belt (at least 8 additional pounds) wraped around it in the other? How does that person come into action as quickly as the gunner in game does? It may have been possible if the MG34 had a top mounted sling like the Bren or BAR did which assisted in walking fire, the MG34 (and MG42) have a bottom mounted sling which is of absolutely no use in action because the gun hands upside down.
It is not that the DP28 should have more ammo, the MG34 needs less, starting with a smaller belt. MG34 max ammo should be around 300 rounds at most, either 2x150 round belts or more realsitically 3x 100 round belt (because a 100 round belt can be kept from dragging on the ground without resorting to wraping the belt around the gun or yourself).
If you want to see what 250 rounds look like:
Notice the 50 round belt alone (minus the pully thing) is about 3/4ths the length of the 1 meter long K98.
Again, it is not historical, a gunner did not carry 500 rounds on himself and move and react like the MG34 gunner in game does. He could not reload as quickly, he could not raise and fire as quickly, especially if that additional 250 rounds is in a box (because the rounds in the box are not evne linked into a single belt).
And I don't need to be told how to use the DP, I have a confortable 3 k/d ratio with it and routinely get 40-50 kills a map with the weapon.